Re: LUDecomposition
- To: mathgroup at smc.vnet.net
- Subject: [mg117735] Re: LUDecomposition
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Wed, 30 Mar 2011 04:16:20 -0500 (EST)
(a) The outputs are NOT the same:
LUDecomposition[{{1, 2}, {3, 4}}]
{{{1, 2}, {3, -2}}, {1, 2}, 1}
LUDecomposition[{{3, 4}, {1, 2}}]
{{{1, 2}, {3, -2}}, {2, 1}, 1}
(b) Alpha IS wrong, as you say, on the second matrix.
(c) The documentation buries far down the page -- and why, one wonders???
-- the critical info that l.u is not the original matrix, but a
PERMUTATION of it:
m = {{1, 2}, {3, 4}};
{lu, p, c} = LUDecomposition@m
l = LowerTriangularize[lu, -1] + IdentityMatrix@2;
u = UpperTriangularize@lu;
l.u == m[[p]]
{{{1, 2}, {3, -2}}, {1, 2}, 1}
True
m = {{3, 4}, {1, 2}};
{lu, p, c} = LUDecomposition@m
l = LowerTriangularize[lu, -1] + IdentityMatrix@2;
u = UpperTriangularize@lu;
l.u == m[[p]]
{{{1, 2}, {3, -2}}, {2, 1}, 1}
True
Bobby
On Tue, 29 Mar 2011 06:58:37 -0500, Kevin <kjslag at gmail.com> wrote:
> LUDecomposition[{{1, 2}, {3, 4}}]
> and
> LUDecomposition[{{3, 4}, {1, 2}}]
> both give the same output:
> {{{1, 2}, {3, -2}}, {1, 2}, 1}
>
> Only the output for the first matrix is correct.
>
> Alpha gives the same incorrect results for the 2nd matrix
> correct 1st matrix:
> http://www.wolframalpha.com/input/?i=LUDecomposition+{{1%2C2}%2C{3%2C4}}
> incorrect 2nd matrix:
> http://www.wolframalpha.com/input/?i=LUDecomposition+{{3%2C4}%2C{1%2C2}}
>
--
DrMajorBob at yahoo.com